By using first-principles methods based on density functional theory we revisited the zero-temperature phase diagram of stoichiometric SrCoO3, a ferromagnetic metallic perovskite that undergoes significant structural, electronic, and magnetic changes as its content of oxygen is decreased. We considered both bulk and epitaxial thin film geometries. In the bulk case, we found that a tetragonal P4/mbm phase with moderate Jahn–Teller distortions and a c/a ratio of is consistently predicted to have a lower energy than the thus far assumed ground-state cubic Pmm phase. In thin films, we found two phase transitions occurring at compressive and tensile epitaxial strains. However, in contrast to previous theoretical predictions, our results show that: (i) the phase transition induced by tensile strain is isostructural and involves only a change in magnetic spin order (that is, not a metallic to insulator transformation), and (ii) the phase transition induced by compressive strain comprises simultaneous structural, electronic and magnetic spin order changes, but the required epitaxial stress is so large (<−6%) that is unlikely to be observed in practice. Our findings call for a revision of the crystallographic data obtained in fully oxidised SrCoO3 samples at low temperatures, as well as of previous first-principles studies.